This Exam FM sample reference tests Redington Immunization. Matching present value and Macaulay duration yields 47,466.39 of assets and an investment of 14,239.92 in Bond A, choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A does not satisfy both the 47,466.39 present-value total and the 20.5-year duration equation.
BChoice B results from treating the amount in Bond C as y rather than twice y.
CChoice C is the amount invested in Bond B, not Bond A.
DChoice D is not reproduced after substituting x = L minus 3y. Both the value and duration constraints are required.
Original practice · fully worked
Original variant: duration matching for a conservation reserve
A conservation trust must pay 120,000 in 11 years and discounts at 6% annually. It funds the obligation with assets having Macaulay durations 5, 10, and 18 years. The amount in the 18-year-duration asset is 1.5 times the amount in the 10-year-duration asset. Find the amount invested in the 5-year asset.
A 15,481
B 20,736
C 24,512
D 29,105
E 36,822
Variant answer in brief
Present-value and duration matching give 24,511.75 in the 5-year-duration asset, which is choice C.
Setup
Setup
Let x be the amount in the 5-year asset and y the amount in the 10-year asset. The third amount is 1.5y.
L=120000(1.06)−11=63214.50
x+2.5y=L
Model
Model
Match the portfolio's dollar duration to the 11-year liability.
5x+10y+18(1.5y)=11L
Compute
Compute
Eliminating x gives y = 15,481.10 and x = 24,511.75.
5(L−2.5y)+37y=11L
y=15481.10
x=63214.50−2.5(15481.10)=24511.75
Answer
Answer
The 5-year-duration asset receives approximately 24,512, which is choice C.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
